Both houses of Congress backed the sanctions bill, which also includes measures against Iran and North Korea.
Asked if Russian President Vladimir Putin had authorized the move, Peskov said such measures are "impossible without the President's permission".
The bill was passed overwhelmingly in the Senate and House by veto-proof margins.
The bill, which includes a provision that allows Congress to stop any effort by Mr Trump to ease existing sanctions on Russian Federation, will now be sent to the White House for him to sign into law or veto.
The U.S. Embassy in Moscow, with a monument to Russian revolutionary workers in the foreground Friday, July 28, 2017.
President Vladimir Putin had warned on Thursday that Russian Federation had so far exercised restraint, but would have to retaliate against what he described as boorish and unreasonable USA behaviour.
Republicans on Capitol Hill had downplayed the notion that Trump would actually consider vetoing the sanctions bill.
The ministry says the US has until September 1 to cut the number of its staff at the Moscow embassy and at three consulates to match the exact number of Russian diplomats who are working in the USA - 455 people, according to the ministry's announcement.
It is not believed that US President Donald Trump supports the new sanctions, often arguing against the findings of US intelligence agencies that high officials in the Kremlin ordered a campaign to disrupt the 2016 US presidential election in his favour.
Secretary of State Rex Tillerson said on Saturday that he was optimistic the new sanctions could be the starting point of an improved relationship with Moscow.
Beebe said Trump's signature will confirm to the Russians "that he's lost control of Russia policy". However, Mr Putin's comments on Sunday were the first to make clear the number of USA envoys he intends to force to leave. That included Russian citizens and USA citizens.
The previous statement had also said that a summer house and warehouse used by the United States embassy in Moscow would be closed down.
The EU and United States previously worked together to impose sanctions in the wake of Russia's annexation of Crimea in March 2014, overcoming division on how far to go in punishing Moscow. "They're going to hurt us on issues like North Korea, Venezuela, Nicaragua, Cuba", he said.
One thing is clear, Beebe said.